English

Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions

Functional Analysis 2007-05-23 v1

Abstract

We give a simple proof of the Kernel theorem for the space of tempered ultradistributions of Beurling - Komatsu type, using the characterization of Fourier-Hermite coefficients of the elements of the space. We prove in details that the test space of tempered ultradistributions of Beurling - Komatsu type can be identified with the space of sequences of ultrapolynomal falloff and its dual space with the space of sequences of ultrapolynomial growth. As a consequence of the Kernel theorem we have that the Weyl transform can be extended on a space of tempered ultradistributions of Beurling - Komatsu type.

Keywords

Cite

@article{arxiv.math/0702093,
  title  = {Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions},
  author = {Z. Lozanov-Crvenkovic and D. Perisic},
  journal= {arXiv preprint arXiv:math/0702093},
  year   = {2007}
}

Comments

accepted for publication in Integral transforms and special functions